Once again, The Times Magazine looks back on the past year from our favored perch: ideas. Like a magpie building its nest, we have hunted eclectically, though not without discrimination, for noteworthy notions of 2009 — the twigs and sticks and shiny paper scraps of human ingenuity, which, when collected and woven together, form a sort of cognitive shelter, in which the curious mind can incubate, hatch and feather. Unlike birds, we can also alphabetize. And so we hereby present, from A to Z, the most clever, important, silly and just plain weird innovations we carried back from all corners of the thinking world. To offer a nonalphabetical option for navigating the entries, this year we have attached tags to each item indicating subject matter. We hope you enjoy.